{"id":129,"date":"2023-08-01T12:07:37","date_gmt":"2023-08-01T10:07:37","guid":{"rendered":"https:\/\/actilud.com\/info\/en\/?p=129"},"modified":"2025-03-29T13:10:12","modified_gmt":"2025-03-29T12:10:12","slug":"repercussion","status":"publish","type":"post","link":"https:\/\/actilud.com\/info\/en\/repercussion\/","title":{"rendered":"Repercussion"},"content":{"rendered":"

Repercussion is one of the most powerful and simplest techniques to implement when a zebra puzzle has multiple grids. It starts with a true sign on a central grid and projects an entire row into another grid. The row can contain false signs, true signs, and even Booleans.<\/strong><\/p>\n

True sign on a central grid<\/h1>\n

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The central grids are yellow.<\/figcaption><\/figure>\n

Please note that a peripheral<\/em> grid is a grid to the right or below a central grid; therefore the grid (teen, duration) is peripheral for the grid (teen, yacht), but it is central for the grid (teen, age).<\/p>\n

If a true sign is in one of the central grids, it acts as a kind of pivot<\/em> for the row or column of the corresponding grids. Let’s see this with an example:<\/p>\n

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Jessie drives a black yacht and is 17 years old. The implication is easy to find: the driver of the black yacht is 17 years old.<\/p>\n

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It’s as if we duplicated the line (Jessie, age) and rotated it towards the column (Black, age), the center of rotation (=the pivot) being the box (Jessie, Black):<\/p>\n

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Fig. 1<\/figcaption><\/figure>\n
Fig. 1<\/figcaption><\/figure>\n

Once the rotation is done, we of course fill the empty boxes near the true sign in the <\/em>\u201c17 years\u201d<\/em> line with false boxes .<\/em><\/p>\n

This is the technique of repercussion: the contents of one row are reflected on another, taking into account the pivot. It’s a powerful technique that allows you to quickly fill rows, as we see in the example below.<\/p>\n

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 <\/p>\n

It is important to understand that the impact is two-way.<\/em> <\/strong> Here, what is in the column (Duration, blue) is reflected in the row (Garry, duration) and vice versa:
\n<\/strong><\/p>\n

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Fig. 2<\/figcaption><\/figure>\n
<\/figure>\n

Now, all you have to do is apply the complement technique to discover that Garry drives for 40 minutes. Which wasn’t entirely obvious at first!<\/p>\n

True sign on a peripheral grid<\/h1>\n

This time there will not be a rotation, but a translation:<\/p>\n

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 <\/p>\n

If we look at this grid, we see that Bill is 14 years old, but his yacht is neither blue, black, nor yellow. We can therefore deduce that the 14-year-old teenager does not drive these colors. Conversely, we see that the 14-year-old teenager does not drive a red yacht. However, since Bill is 14, he therefore does not drive a red yacht.<\/p>\n

This reasoning can be visualized by merging<\/em> the two lines (Bill, Yacht) and (14 years, Yacht):<\/p>\n

<\/figure>\n
\n

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Fig. 3<\/figcaption><\/figure>
<\/figcaption><\/figure>\n

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 <\/p>\n

Where we see, after using the complement technique, that Bill is driving a green yacht.<\/p>\n

Please note: these cases are examples; a true<\/em> sign does not always appear!<\/p><\/blockquote>\n

Of course, the translation can also apply to columns:<\/p>\n

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Fig. 4<\/figcaption><\/figure>\n

Here we conclude that the driver of the green yacht, as well as the one who drives for 50 minutes, is neither 13, nor 14 nor 17 years old.<\/p>\n

The impact: find the grids concerned<\/h1>\n

For a rotational or translational impact to be possible, the two grids whose rows rotate or translate must have the same header in common<\/strong> .<\/p><\/blockquote>\n

Fig 1: This is the age header
\n<\/em> Fig 2: This is duration header
\nFig 3: <\/em>yacht header
\n<\/em> Fig 4: age header<\/em><\/h6>\n